Double cogged V-belt for variable speed drive

ABSTRACT

A double-cogged V-belt with the upper and lower cog profiles symmetric and having lines (“L”) and arcs (“A”) connected according to a sequence from the center of a root to the center of an adjacent cog of L 1 -A 1 -L 2 -A 2 -L 3  for the upper profile and A 3 -L 5 -A 4 -L 6 , and with at least one upper root and one lower root substantially aligned with each other, and with the sum of the length of L 1  plus the radius of A 1  equal to or within 20% of the radius of A 3 . The upper and lower pitches may be equal and all the roots aligned, or there may be more upper cogs than lower cogs. Some or all arcs and lines may be connected tangentially.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to a double-cogged V-belt, moreparticularly to a double-cogged V-belt with aligned upper and lower cogshaving a particular combination of cog profiles, and specifically such aV-belt adapted for a variable speed transmission.

2. Description of the Prior Art

The belt plays an important role in the operation of variable speedpower transmission systems or drives, such as used in scooters,motorcycles, snowmobiles, all-terrain vehicles, cars and industrialapplications. In one exemplary design of variable speed transmission(“VST”), the belt is a flexible element which connects two pairs ofsheaves through friction to transmit power from the driving shaft to thedriven shaft. Each pair of sheaves includes a fixed sheave and a movablesheave. By controlling the axial movement of movable sheaves, the speedand torque ratio may be changed. During operation, the belt sustainsextreme longitudinal tension and bending and transverse compression. Toachieve maximum performance, efficiency, and durability, one of the mainchallenges the belt design faces is meeting contradictory requirements,namely high longitudinal flexibility but high transverse stiffness whilemaintaining proper side contact. The general approach to this challengehas been to form alternating thick and thin sections on one or bothsides of the belt, known as cogs or teeth, and roots, also known asvalleys, grooves or notches, respectively. Cogs are intended to providethe thickness and stiffness needed for transverse stiffness, while theroots or notches are intended to provide the needed longitudinal bendingflexibility. Cogs may be formed or applied on the inside or lower sideof the belt, or cogs may be applied to the outside, i.e., the backsideor upper side of the belt. Alternately, cogs may be applied to both thelower and upper side of the belt, resulting in a double-cogged belt.

The challenge for conventional V-belts for fixed sheaves or single-speeddrives is similar, but not as severe. V-belts for VST generally need tobe relatively wider and thinner than V-belts for fixed drives in orderto accommodate a range of movement radially inward and outward in thevariable sheaves. The resulting relatively wide aspect ratio of VSTbelts makes transverse stiffness more difficult to achieve, especiallywith the shifting movements placing increased transverse loads on thebelt. On the other hand, since V-belts in fixed drives need not move inor out, the aspect ratio of the belt can be such that sufficienttransverse stiffness is more easily achieved. Thus, while the use ofcogs or notches is common to both fixed- and variable-speed V-belts, afixed-speed V-belt cog design may not perform well in a VST.

Representative of the art is U.S. Pat. No. 4,276,039 which discloses adouble-cogged V-belt for fixed drive with aligned upper and lower cogs.Such early designs have become disfavored because of perceived problemscaused by alignment of the cogs and particularly alignment of the roots.Alignment of the upper and lower roots creates relatively thin websections between the cogs where bending stresses may be highlyconcentrated and where bending radii can become very small. This resultsin cracking of the belt body in the root areas, cord fatigue and earlyfailure. U.S. Pat. No. 4,276,039 applies a canvas cover over both lowerand upper belt surfaces to help prevent cracking.

Also representative of the art is U.S. Pat. No. 4,708,703, whichdiscloses a V-belt for a VST with aligned upper and lower teeth andgrooves. The teeth are preferably covered at their tops with areinforcing and stiffening element to deal with the problem of buckling.

The art contains many attempts to optimize the profile, including theshape, pitch, depth, alignment, and the like, of the upper and lowercogs of double-cogged V-belts. U.S. Pat. No. 6,620,068 discloses araw-edge double-cogged V-belt for variable speed drives havingcurvilinear cogs on the inside and outside. The number of outside cogsare twice the number of and aligned with the inside cogs. JP2002-089631A discloses a dual cog V-belt with more upper cogs than lowercogs, but less than twice as many so that the alignment or phase of theupper and lower cogs is variable.

A number of patents teach that the upper and lower cogs should bestaggered, i.e., exactly 180° out of phase and of equal pitch or number.U.S. Pat. No. 1,890,080 discloses staggered rounded cogs of equal sizeand shape. U.S. Pat. No. 2,699,685 discloses staggered blocky-shapedcogs of equal size and shape with the grooves of one section verticallyopposite the cogs of the other section in order to avoid weak spots andso that the thickness of the belt is the same all over.

JP 2002-031192A discloses a variation on a staggered double-coggedV-belt for VST applications wherein equal-numbered upper and lower cogsare not exactly in phase or out of phase, but phase shifted an amountsomewhere in between, preferably from a tenth to half of the pitch. Thatpublication teaches that lower and upper cog parts should not align orcorrespond so the belt thickness does not get extremely small thuspreventing stress concentration and early crack initiation in thatregion. Finite element method (“FEM”) analysis was apparently used todesign an improved phase-shifted staggered profile and to confirm thiseffect. Increased phase shift up to half a pitch resulted in reducedroot cracking.

In designs such as disclosed in JP 2002-031192A and JP 2002-089631A inwhich there are more upper cogs than lower cogs, the alignment of theupper and lower cogs is variable. In such a design, unequal pitchesresults in a “weak link” at the position around the belt where the upperand lower roots are most closely aligned. Root cracking may be observedto begin at this aligned root position. Even so, this design seems to bethe most optimized design in the current market for double-coggedvariable-speed V-belts.

Reference is made to co-pending U.S. patent application Ser. No.12/217,026 filed Jul. 1, 2008, the contents of which are incorporatedherein by reference in their entirety.

SUMMARY

The present invention is directed to systems and methods which provideimproved double-cogged V-belts, or provides improved double-coggedV-belts for variable-speed drives.

The present invention is directed to a double-cogged V-belt with theupper and lower cog profiles symmetric and having lines (“L”) and arcs(“A”) connected according to a sequence beginning from the center of aroot and extending to the center of an adjacent cog, the sequence beingL1-A1-L2-A2-L3 for the upper profile and L4-A3-L5-A4-L6 for the lowerprofile, and with the sum of the length of L1 plus the radius of A1equal to or within 20% of the sum of the length of L4 plus the radius ofA3, and with at least one upper root and one lower root substantiallyaligned with each other.

In one embodiment the upper and lower pitches may be equal and all theroots substantially aligned. In another embodiment there may be moreupper cogs than lower cogs. The ratio of the number of upper to lowercogs may be up to 1.3, or from 1.1 to 1.3.

In yet another embodiment, L4 has zero length, so that the lower profilehas the sequence ALAL. In variations of this embodiment, the upper andlower pitches may be equal and all the roots substantially aligned, orthere may be more upper cogs than lower cogs.

In various embodiments, some or all arcs and lines may be connectedtangentially. For example, lines L1 and L2 may connect tangentially witharc A1, and said lines L4 and L5 may connect tangentially with arc A3.Preferably L1, L3, L4, and L6 connect tangentially with their mirrorimages at the centers of the roots and centers of the cog tips, so thatthe roots and tips are flat and smooth.

In various embodiments, the flanks of the cogs may be at an angle sothat the included angle between opposing cog flanks is in the range offrom about 10 to about 30 degrees.

Embodiments of the invention are particularly suited to V-belts forvariable speed transmissions when the top width of the belt is abouttwice the overall thickness of the belt. It may also be advantageous forthe pulley contact faces of the V-belt to have a first planar surfacedisposed at a first angle for engaging a sheave and a cooperating secondplanar surface disposed at a second angle that does not engage with asheave surface.

The inventive belt exhibits various advantages over prior artdouble-cogged V-belt designs. Flexibility is improved withoutsignificantly increasing susceptibility to root cracking, and improvedcrack resistance is seen in the lower cog roots especially. Consistencyof performance is improved.

The foregoing has outlined rather broadly the features and technicaladvantages of the present invention in order that the detaileddescription of the invention that follows may be better understood.Additional features and advantages of the invention will be describedhereinafter which form the subject of the claims of the invention. Itshould be appreciated by those skilled in the art that the conceptionand specific embodiment disclosed may be readily utilized as a basis formodifying or designing other structures for carrying out the samepurposes of the present invention. It should also be realized by thoseskilled in the art that such equivalent constructions do not depart fromthe spirit and scope of the invention as set forth in the appendedclaims. The novel features which are believed to be characteristic ofthe invention, both as to its organization and method of operation,together with further objects and advantages will be better understoodfrom the following description when considered in connection with theaccompanying figures. It is to be expressly understood, however, thateach of the figures is provided for the purpose of illustration anddescription only and is not intended as a definition of the limits ofthe present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form part ofthe specification in which like numerals designate like parts,illustrate embodiments of the present invention and together with thedescription, serve to explain the principles of the invention. In thedrawings:

FIG. 1 is a partial side view of an embodiment of the invention;

FIG. 2 is a cross sectional view along line 2-2 of FIG. 1;

FIG. 3 another partial side view of the embodiment of FIG. 1;

FIG. 4 illustrates a cog profile nomenclature system as applied to theembodiment of FIG. 1;

FIG. 5 illustrates the cog profile nomenclature system as applied to asecond embodiment of the invention;

FIG. 6 illustrates the cog profile nomenclature system as applied to athird embodiment of the invention;

FIG. 7 illustrates the cog profile nomenclature system as applied to aprior art cog profile;

FIG. 8 illustrates the cog profile nomenclature system as applied toanother prior art cog profile; and

FIG. 9 illustrates the cog profile nomenclature system as applied toanother prior art cog profile.

FIG. 10 illustrates the cog profile nomenclature system as applied to afourth embodiment of the invention.

DETAILED DESCRIPTION

To achieve maximum performance, efficiency, and durability in a VST, thebelt has to be designed with high flexibility but high transversalstiffness while maintaining proper side contact and low stressconcentration. To satisfy these special requirements at some level, aV-belt may be adapted with a single set of lower cogs on the inside 40of the belt. In a VST application requiring higher transmitting power, adouble cogged V-belt design, in which additional cogs are added on theupper or back side 30 of a belt, may be used to further increasetransversal stiffness while still maintaining high flexibility andsuitable contact area. For both designs of single cog and double cog VSTbelts, optimal geometries of cog profiles and cord position are crucialbut not easily discovered, as indicated by the large number of proposalsfound in the art.

Usually, the profile of each cog is symmetric about the cog center andis a combination of straight line segments and arcs. A nomenclaturesystem is used herein and in the claims to help identify and categorizeprofiles found in the art and embodiments of the present invention. Inthis system “A” represents an arc that is a component of a profile and“L” represents a line. If adjacent arcs and/or lines are connected, butnot tangentially connected, a “+” sign is used to indicate theconnection. Another way to describe non-tangentially connected arcand/or line segments is that the first derivative is not continuous atthe point of connection. If two adjacent arc and/or line segments areconnected tangentially in a cog profile, then no sign is used betweenthe two letters designating those segments in the nomenclature systemused herein. A sequence numeral may be used in association with theletters L and/or A to differentiate a number of lines or arcs in asequence defining a given profile. For example, “L1” may refer to thefirst line segment in a profile, and depending on the context, “L1” mayalso refer to the length of that line segment. Likewise, “A1” may referto the first arc in a sequence representing a profile, and “R1” mayrefer to the radius of that arc. For symmetric profiles, only half arepeating unit need be described as the other half is a mirror image ofthe first half. In the system used herein, the profile description willbegin with a root center and end with a cog tip center. Other featuresof the nomenclature system will be described as needed below.

The invention is directed to double-cogged V-belts with an upper cogprofile having the sequence LALAL, and a lower cog profile also havingthe sequence LALAL. Thus, the root or valley, represented by the first Lin both the upper and lower profile is substantially flat. Also theflank of the cog in both upper and lower profiles is flat and the tip ofthe cog in both upper and lower profiles is flat. Each flat portion isconnected by an arc. By substantially “flat” is meant that the profileportion is straight when the belt is laid out flat, which is called the“rack” form of the profile. Thus, when placed in its natural state whichmay be a circular band configuration, a flat segment may actually followthe curvature of the cord line or the natural curvature of the belt. Ingeneral, all arcs and line segments must be of finite and non-zeroradius and length, unless explicitly stated otherwise as a special case.If this condition is not met, then the profile should be representedotherwise according to the nomenclature convention used herein. The cogsare disposed along the entire length of the belt.

It will be convenient to number the lines and arc of the profiles of theinventive belt. Thus, the upper cog profile may be represented with thesequence L1-A1-L2-A2-L3 from the center of a root to the center of anadjacent cog. Likewise, the lower cog profile may be represented withthe sequence L4-A3-L5-A4-L6 from the center of a root to the center ofan adjacent cog. The embodiment of FIG. 3 illustrates the location andconnections between these arcs and lines forming the cog profiles of adouble-cogged V-belt. The invention is directed to such double-coggedV-belts with at least one upper root aligned with at least onecorresponding lower root. Also, in the inventive belts, the sum of thelength of L1 plus the radius of A1 is equal to or within 20% of the sumof the length of L4 plus the radius of A3. One specific exception to therule that all arcs and line segments must be of finite and non-zeroradius and length, is that in various embodiments, L4 may be of zerolength. Another specific exception to the same rule is that L2 may be ofzero length in specific embodiments.

Detailed features of the invention and characteristics of embodiments ofthe invention may be defined and illustrated with reference to FIG. 1,FIG. 2, and FIG. 3. Referring to FIG. 1, double-cogged V-belt 10includes tensile layer 16 sandwiched between overcord layer 14 andundercord layer 12 making up the main body of the belt. Thedouble-cogged V-belt shown in FIGS. 1-3 also has lower cogs 18 and uppercogs 20 protruding from the main belt body. Upper cogs 20 include tip17, flank 26 and valley or root 22. Likewise lower cogs 18 include tip19, flank 36 and root 32. The double-cogged V-belt of FIG. 1 and FIG. 3is drawn in rack form, i.e., flat and without curvature of the tensilelayer.

FIG. 2 shows a section of the V-belt of FIG. 1, cut along the line 2-2in FIG. 1. The overall belt width is called the top width and identifiedas “TW”. The overall thickness of the belt is identified as “T₀”. Thepulley contact faces or side surfaces 42 of the V-belt are cut at anangle α/2 with respect to the vertical axis of the belt, which shouldgenerally coincide with the vertical axis of a pulley or drive system.Thus, a pair of opposing belt side surfaces 42 describe an includedangle α. Each side surface 42 engages a sheave during operation, withthe sheave angles also substantially equal to α/2.

In embodiments of the invention, it may be advantageous for each cog tofurther include an opposing pair of second side surfaces 44 which aredisposed toward a lower cog tip 19 and which are cooperating with thefirst side surfaces 42. Each pair of second side surfaces 44 describesan included angle γ. Angle α may be in the range of approximately 15° to50° (so about 7° to about 25° per pulley sheave angle). Angle γ may bein the range of approximately 25° to 65°. Namely, γ=α+(2×relief angle).The “relief angle” may be equal to or greater than approximately 5° andmay be defined as (γ/2−α/2). It is believed the cooperating nature ofthe first side surfaces and second side surfaces results in asignificant reduction in noise generated by the belt during operation.All numeric values used in this specification to describe the inventionare examples only and are not intended to limit the breadth orapplicability of the invention unless otherwise stated. By way ofexample, the second side surface 44 may comprise a relief angle ofapproximately 5° which prevents the second side surface 44 from comingin contact with a sheave. Assuming an angle α of 20°, this gives anangle γ of 30°. The cog tip cut height, (“h_(t)”) in FIG. 2, may beadjusted as needed, for example, it may be about 1 to 2 mm.

FIG. 3 identifies additional dimensional characteristics ofdouble-cogged V-belt 10. The tensile layer thickness, or tensile corddiameter, may be identified as “D”. The thickness of the overcord layeris t₂ and the thickness of the undercord layer is t₁. The distance fromthe upper cog tip to the center of the tensile layer is identified as“PLD₂”, and the distance from the lower cog tip to the center of thetensile layer is identified as “PLD₁”. PLD stands for pitch linedifferential and is based on a common simplifying assumption that thebelt's neutral axis in bending, i.e., its pitch line, occurs at thecenter of the tensile layer. The web thickness “W” is the distancebetween an upper root and lower root that are aligned. The depth of anupper root, or equivalently the height of an upper cog, is identified as“H2”, and the depth of a lower root, or equivalently the height of alower cog, is identified as “H1”. The pitch, i.e., the profile repeatdistance, is identified as the distance between two adjacent roots,which is “P2” for the upper profile and “P1” for the lower profile. Thelines and arcs making up the profile were introduced previously. Thelines “L2” making up the opposing flanks of an upper cog form anincluded angle “β₂”. The lines “L5” making up the opposing flanks of alower cog form an included angle “β₁”. Other features and/orrelationships between features may be self-evident from the figures. Forexample, T₀=PLD₁+PLD₂=H1+H2+W. Also, W=t₁+D+t₂.

In various embodiments, L4 may have zero length, so that the lowerprofile has the sequence ALAL. In variations of this embodiment, theupper and lower pitches may be equal and all the roots substantiallyaligned, or there may be more upper cogs than lower cogs. Theseembodiments will be described in more detail later.

In various embodiments, some or all arcs and lines may be connectedtangentially or at least in a smooth transition. Preferably L1, L3, L4,and L6 connect tangentially with their mirror images at the centers ofthe roots and centers of the cog tips, so that the roots and tips areflat and smooth. Also preferably, lines L1 and L2 may connecttangentially with arc A1 (24 in FIG. 1), and/or said lines L4 and L5 mayconnect tangentially with arc A3 (34 in FIG. 1). These connectionsbetween the roots and flanks of the cogs are particularly importantbecause of the stress concentrations that occur there during operationof the belt.

On the other hand, the stresses at the tips of the cogs, including inthe neighborhood of A2 (28 in FIG. 1), L3, A4 (38 in FIG. 1) and L6, aregenerally of much less importance to belt life which is associated withcog root crack, therefore in embodiments of the invention, L2 and L3need not connect tangentially with A2, L5 and L6 need not connecttangentially with A4, and R2 may be made as small as possible tomaximize the size of the cogs tips and thereby maximize the transversestiffening effect of the cogs on the belt. Still, R2 and R4 should befinite, making the cog tips at least slightly rounded, in order to avoidmanufacturing issues due to sharp corners or non-smooth transitions.

In various embodiments, the included angle between opposing cog flanksmay be in the range of from about 10 to about 30 degrees. Either or bothincluded angles, β₁ and/or β₂, may be in the range of 10 to 30 degrees.

Embodiments of the invention are particularly suited to V-belts forvariable speed transmissions when the top width of the belt is abouttwice the overall thickness of the belt. For single-speed V-belts, theratio of top width to overall thickness may be closer to unity. Theinvention is not particularly limited in applicability, although it isthought to be of particular utility for VST belts.

A description of three preferred embodiments and a number of additionalfeatures which may be found in one or more of the preferred embodimentsfollows.

As mentioned above, the invention is directed to double-cogged V-beltswith LALAL-type upper and lower profiles. Such a profile is illustratedin FIG. 4, which shows upper profile 41 including sequence LALAL, andlower profile 43 also including sequence LALAL. At least one upper rootis aligned with at least one corresponding lower root as also shown inFIG. 4. Also, in the inventive profiles the sum of the length of L1 plusthe radius of A1 is equal to or within 20% of the sum of the length ofL4 plus the radius of A3, i.e., 0.8≦(L1+R1)/(L4+R3)≦1.2. This sum is anapproximation of the width of the root, or the distance between adjacentcogs near the base of the cogs. When the upper and lower cogs havesimilar spacing, i.e., upper and lower root widths are within about 20%of each other, and when at least one pair of roots are aligned and theroots have linear or flat portions, then the belt will be flexible. Itis believed that flexibility is the primary or first consideration toaddress in designing a long life, high performance VST belt. This is incontrast to teaching in the art that root alignment is not desirable.Another advantage of the roots having linear or flat portions is thatalignment is easier to achieve during belt manufacture. The wider theroot, the more forgiving the manufacturing process will be in terms ofroot alignment and obtaining the resulting benefits in flexibility.Thus, the substantial alignment of the upper and lower roots may not orneed not necessarily be perfect. It may be sufficient for the linear orflat portions of the upper and lower roots to overlap somewhat inembodiments of the invention. In contrast, very narrow, curved rootsmust be precisely aligned to realize any benefit in flexibility, leadingto manufacturing problems.

In a first more specific embodiment of the above invention, the roots ofthe lower profile have no flat portion. In other words, L4=0, orequivalently, the lower cog profile is of the sequence ALAL. In thisembodiment, the alignment of a lower and upper root is still relativelyeasy to achieve, since the midpoint of the lower root need only bealigned somewhere within the linear or flat portion L1 of the upperroot. Such a profile is illustrated in FIG. 5, which shows upper profile45 including sequence LALAL, and lower profile 49 including sequenceALAL. Again, at least one upper root is aligned with at least onecorresponding lower root.

In a second more specific embodiment of the invention the belt has equalnumbers of upper and lower cogs. In other words, P1 and P2 are equal,when the belt is disposed in rack form. It should be understood that abelt wrapped around a sheave has compressed lower dimensions andexpanded upper dimensions, so for convenience the belt is describedherein in rack form. Since the number of upper cogs, N2 and the numberof lower cogs N1 are equal and at least one set of roots are aligned,the entire upper and lower profiles are substantially aligned. Again,this is contrary to much recent teaching in the art. As discussed above,root-to-root alignment results in the most flexible belt designpossible. Maintaining a flat or linear segment in the upper and lowerroot makes alignment easier during manufacture. In comparison to astaggered profile design as described in the background section above,the aligned design of the present invention is so much more flexiblethat the web thickness “W” can be increased somewhat if desired forexample to increase transverse strength. Thus, though the belt portionwhere the roots are aligned may represent the “weak link” of the belt,it is believed that by aligning all the roots, the strength of the weaklink can be improved along with the flexibility, resulting in an overallgain in performance. In addition, since the geometry is consistent fromcog to cog, so is the deformation and load, and the performance and lifeof the belt is thus is improved. Moreover, the highest stress regions inconventional designs are associated with the inflexible cog-to-rootaligned portions of the belt, which are completely eliminated in theroot-to-root aligned embodiment.

In variations of the second specific embodiment, it may be desirable tolimit L4 to zero length, or equivalently, the lower cog profile is ofthe sequence ALAL, as in the first specific embodiment above. When L4=0,it may also be desirable to further define the width of the upper rootrelative to the width of the lower root so that the sum of the length ofL1 plus the radius of A1 is greater than or equal to and within about20% of the radius of A3, i.e., 1.0≦(L1+R1)/R3≦1.2. This latterlimitation may prevent some difficulty aligning roots duringmanufacture.

In a third more specific embodiment of the invention the belt still hasLALAL-type upper and lower profiles, and at least one upper root isaligned with at least one corresponding lower root, and the sum of thelength of L1 plus the radius of A1 is equal to or within 20% of the sumof the length of L4 plus the radius of A3. However, in this thirdembodiment, the belt has a greater number of upper cogs than lower cogs.In other words, P1>P2, when the belt is disposed in rack form. Such aprofile is illustrated in FIG. 6, which shows upper profile 46 includingsequence LALAL, and lower profile 47 including sequence ALAL. Since onlyhalf a pitch is shown, the pitches and the phase shift, “ΔP”, areindicated as divided by 2. The ratio of N2 to N1 is not particularlylimited but may preferably be in the range 1.0 to 1.3 or from about 1.1to about 1.3. Since the number of upper cogs, N2 and the number of lowercogs N1 are not equal, but at least one set of roots are aligned, notthe entire upper and lower profiles will be substantially aligned.However, with the upper roots having some linear or flat width, and withN2 not too much larger than N1, there may still be a substantial numberof cogs that are substantially aligned. Moreover, the inventive profileshape is improved and therefore, belts of this embodiment are believedto still exhibit enhanced flexibility and performance over otherconventional profile designs. It should be understood that the lower cogprofile could be of the LALAL type, though the example of FIG. 6 showsit of the ALAL type. This embodiment may encounter lower manufacturingcosts as a result of the pitch difference and resulting less-criticalalignment of profiles.

It should be understood, that one or more of the features mentionedearlier may also be found in variations of the invention according toany of the three specific embodiments described herein. This includeswithout limitation the included angle of the cog flanks, the relativetop width and overall thickness, the relief angle cut in the contactfaces, and the various smooth connections of the profile arcs and lines.

In various embodiments, it may also be useful to permit L2 to be of zerolength, so that the upper profile is of the type LAAL, as illustrated inFIG. 10. This fourth embodiment may be useful in belts in which it isdesired to make the upper cogs relatively short, i.e. H2 is relativelysmall.

V-belts according to the present invention may comprise any suitablematerial or materials. The following material examples are offered byway of example and are not intended to limit the breadth orapplicability of the invention. Tensile layer 16 may have individualtwisted cords of high tensile fibers such as glass, carbon, metal,polyester, nylon, aramid (including PBO), and blends or composites ofthe foregoing and the like. The tensile layer may be woven, fabric, tirecord, or the like as desired. The belt body may be of any desiredcomposition, but exemplary materials are rubber compounds based onelastomers such as natural rubber, polychloroprene, polyisoprene,styrene-butadiene rubber, ethylene-alpha-olefin elastomers, nitrilerubber, polyurethane elastomer, various thermoplastic elastomers, andthe like. These elastomers may be compounded as known in the art withvarious fillers, short fiber fillers, plasticizers, oils, process aids,anti-oxidants, anti-ozonants, curatives, coagents, and the like. Otherreinforcing layers may incorporated into the belt besides the tensilelayer, such as other textile layers which may woven, non-woven, knit, ordiscontinuous fiber layers, oriented or not oriented as known in theart. For example, textile layers may be used at any surface of the beltfor example to modify the surface properties, strengthen the resistanceto crack formation and/or propagation, or the like.

The invention may be made according to known methods of belt making,including for example, building up the various layers of textiles,elastomers, and tensile members, upright or inverted, on a cylindricalmold or on a mandrel for transfer to a mold. The mold may have the cogprofile formed therein and/or so-called “matrix” may be used to producea cog profile. After curing or vulcanization to form a double coggedslab, individual belts may be cut and/or ground therefrom with theproper contact surface angle or angles and inverted if necessary.

The following examples serve to illustrate the advantages of theinventive double-cogged V-belt design over representative other designsfound in the art. In the examples, finite element analysis (“FEA”) wasused to compare various belt designs. In each case the same materialproperties for the belt body material (a typical elastomer compound) andthe tensile layer (a typical aramid tensile cord) were used, so thedifferences in results would be solely attributable to the profiledesign differences. The FEA modeling included running four models foreach belt example to simulate various operational conditions a VST beltsees: a belt bending model, a tension model, an underdrive model, and anoverdrive model. The bending model started with ⅛ length of belt in a45° arc as its natural molded shape, then rotated one end an additional180°, ending in a 225° arc. The tension model started with the same 100mm length of belt in a 90° arc and pulled it straight. The overdrivemodel simulated tensioning the belt between two sheaves by applying ahub load of 1000 N, at sheave diameters representing a high speed ratio,then rotated the driver sheave with 30 Nm of torque on the drivensheave. The underdrive model simulated tensioning the belt between twosheaves by applying a hub load of 1000 N, at sheave diametersrepresenting a low speed ratio, then rotated the driver sheave with 30Nm of torque on the driven sheave.

The dimensions and characteristics of the example belts (Ex. A and Ex.B) are shown in Tables 1-3, along with data for four comparativeexamples (Comp. Ex. 1-4). Table 1 shows the upper cog profile data,Table 2 shows the lower cog profile data, and Table 3 shows additionalgeneral belt geometry data. Ex. A is an embodiment of the currentinvention having upper profile of type LALAL and lower profile of typeALAL, with equal numbers of upper and lower cogs and the profilesaligned root-to-root. Ex. B is an embodiment of the current inventionhaving the same lower cog profile as Ex. A, but the upper profile hasmore cogs than the lower profile. Both examples have L4=0 according toan embodiment of the invention. None of the examples or comparativeexamples have a relief angle as described herein.

The comparative examples are based on V-belts for VST applications foundin the market currently. The cog profiles for Comp. Ex. 1 are shown inFIG. 9, where upper profile 66 is of type A+LAL, and lower profile 68 isof type ALA. The cog profiles for Comp. Ex. 2 are shown in FIG. 7, whereupper profile 62 is of type AAL and lower profile 60 is of type ALA. Thecog profiles for Comp. Ex. 3 are shown in FIG. 8, where upper profile 54is of type A+A and lower profile 56 is of type AL+A. The cog profilesfor Comp. Ex. 4 are not specifically shown in a separate figure but areof previously illustrated types. FIG. 7-9 illustrate lack ofroot-to-root alignment in the comparative examples, for example by phasedifference 64 in FIG. 7 and phase difference 58 in FIG. 8. Also, notethe sharp profile breaks where arcs and/or lines do not meet smoothly ortangentially, for example at points 50 and 52 in FIG. 8.

TABLE 1 Upper Cog Comp. Comp. Comp. Comp. Profile Ex. A Ex. B Ex. 1 Ex.2 Ex. 3 Ex. 4 upper profile LALAL LALAL A + LAL AAL A + A A + A type L1(mm) 0.75 0.5 0 0 0 0 R1 (mm) 1.5 1.5 2.04 2.46 1.45 1.45 A1 (degrees)78 78 49.5 90 69.082 69.777 L2 (mm) 1.86 18.2 1.608 0 0 0 β2 (deg.) 2424 23 0 0 0 R2 (mm) 1 1 1.26 1.03 1.208 1.191 A2 (degrees) 78 78 78.5 9090 90 L3 (mm) 2.178 1.239 1.762 1.352 0 0

TABLE 2 Lower Cog Comp. Comp. Comp. Comp. Profile Ex. A Ex. B Ex. 1 Ex.2 Ex. 3 Ex. 4 lower profile ALAL ALAL ALA ALA AL + A ALA type L4 (mm) 00 0 0 0 0 R3 (mm) 2 2 1.92 2.19 1.98 2.51 A3 (degrees) 78 78 79.04573.918 74 67.05 L5 (mm) 3.308 3.308 2.646 3.337 4.15 3.75 β1 (deg.) 2424 21.91 32.184 32 45.9 R4 (mm) 2.5 2.5 3.17 2.78 3.22 2.32 A4 (degrees)78 78 79.045 73.918 36.334 67.05 L6 (mm) 0.513 0.513 0 0 0 0

TABLE 3 Belt Ex. Ex. Comp. Comp. Comp. Comp. Geometry A B Ex. 1 Ex. 2Ex. 3 Ex. 4 TW (mm) 27 27 29.4 29.4 29.4 29.4 T₀ (mm) 14.6 14.6 14.514.5 14.5 14.5 PLD₂ (mm) 5.4 5.4 4.8 4.8 4.8 4.8 PLD₁ (mm) 9.2 9.2 9.79.7 9.7 9.7 t₂ (mm) 1.223 1.221 1.094 0.904 2.193 2.193 t₁ (mm) 1.8 1.82.379 2.291 3.069 2.681 W (mm) 4.003 4.001 4.453 4.175 6.242 5.854 D(mm) 0.98 0.98 0.98 0.98 0.98 0.98 α (deg) 28 28 28 28 28 28 Belt Length911.1 911.1 876.3 872.7 874.8 871.2 (mm) P1 (mm) 11.206 11.206 11 11.49.91 11.82 N1 (#) 80 80 78 75 86 72 P2 (mm) 11.52 9.126 9.736 9.6845.124 5.104 N2 (#) 80 101 91 91 174 174 N2/N1 1.00 1.26 1.17 1.21 2.022.42 (L1 + R1)/ 1.13 1.00 1.06 1.12 0.73 0.58 (L4 + R3) TW/T₀ 1.85 1.852.03 2.03 2.03 2.03

The results of the FEA models are shown in Table 4. In Table 4, twocolumns of results are presented for Ex. B. Since Ex. B has more uppercogs than lower cogs, the model predictions for both the aligned portionof the profile and the staggered or non-aligned portion of the profileare presented. The column labeled Ex. B-1 provides results for thealigned, root-to-root portion of the belt, while the column labeled Ex.B-1 provides results for the case where a root and a cog are aligned.Since the bending model involves a whole section of belt with both typesof alignment included, only one result is presented. Results for thetension model are not separately provided since the peak stresses are inthe tensile cord layer, and the bending stresses are much less than inthe bending model. For the comparative examples, which also wouldnormally have both extremes, just the worst case result is presented.The results are presented as peak strain energy density (“SED”) in theregion of interest described in the table, namely cog root or cog tip.Also presented is the peak contact friction stress (“CFS”) as describedin the table. Table 4 presents both absolute values of the above and arelative value, i.e. percent difference (“Diff. (%)”) based on the bestof the four comparative examples which is indicated with a “B”.

TABLE 4 Ex. Ex. Ex. Comp. Comp. Comp. Comp. A B-1 B-2 Ex. 1 Ex. 2 Ex. 3Ex. 4 Bending stiffness Stiffness 2 2.2 3.3 3 5.3 4.7 (Nmm/deg) Diff.(%) −32 −25 11 B 44 37 Peak SED at Lower Cog Root Overdrive SED (MPa)0.226 0.228 0.222 0.25 0.263 0.312 0.338 Diff. (%) −9 −9 −11 B 5 25 35Underdrive SED (MPa) 0.399 0.404 0.439 0.454 0.485 0.554 0.597 Diff. (%)−12 −11 −3 B 7 22 31 Peak SED at Lower Cog Tip Overdrive SED (MPa) 0.8520.866 0.888 0.718 0.863 0.896 0.918 Diff. (%) 19 21 24 B 20 25 28Underdrive SED (MPa) 0.534 0.53 0.563 0.457 0.543 0.632 0.669 Diff. (%)17 16 23 B 19 38 46 Peak SED at Upper Cog Root Overdrive SED (MPa) 0.030.033 0.027 0.029 0.023 0.048 0.052 Diff. (%) 29 41 17 24 B 109 126Underdrive SED (MPa) 0.047 0.046 0.045 0.05 0.039 0.087 0.096 Diff. (%)22 18 15 30 B 123 146 Peak CFS at Lower Cog Root Overdrive CFS (MPa)2.23 2.272 2.325 2.458 2.509 2.775 2.85 Diff. (%) −9 −8 −5 B 2 13 16Underdrive CFS (MPa) 3.107 3.131 3.202 3.353 3.405 3.68 3.754 Diff. (%)−7 −7 −5 B 2 10 12 Peak CFS at Lower Cog Tip Overdrive CFS (MPa) 3.8533.875 3.917 3.814 4.033 3.743 4.145 Diff. (%) 1 2 3 B 6 B 11 UnderdriveCFS (MPa) 3.091 3.084 3.161 3.061 3.269 3.312 3.653 Diff. (%) 1 1 3 B 78 19

The FEA analyses on double-cogged variable speed transmission belts haveconfirmed that both exemplary embodiments of Ex. 1 and Ex. 2 are animprovement over the comparative examples. The bending stress resultsconfirm that Ex. 1 and 2 have maximized flexibility, 32% and 25% betterthan the best comparative example, respectively. The SED results confirma reduced peak stress in the lower cog roots under both overdrive andunderdrive conditions, 3% to 12% better than the best comparativeexample. Likewise, the peak CFS level in the lower cog roots issignificantly improved, from 7% to 9% less than the comparativeexamples. The upper cog roots show comparable SED levels to thecomparative examples, but it should be noted that the absolute values ofSED in the upper roots are already much lower than in the lower roots.

The FEA analyses also shows that the peak cog tip strain energy density,namely the SED, increases significantly in the Example belts relative tothe comparative examples, by 16 to 21%. This is not necessarily bad,since cog tips are generally not prone to strain or stress-inducedcracks. Instead, the increased tip stress may indicate that more of theload is being carried by the cog in accordance with one purpose ofhaving cogs.

Thus, the present invention is shown to provide a double-cogged V-belt,in particular for VST applications, with improved flexibility, reducedtendency to develop root cracks, and improved performance consistency.

Although the present invention and its advantages have been described indetail, it should be understood that various changes, substitutions, andalterations can be made herein without departing from the spirit andscope of the invention as defined by the appended claims. Moreover, thescope of the present application is not intended to be limited to theparticular embodiments of the process, machine, manufacture, compositionof matter, means, methods, and steps described in the specification. Asone of ordinary skill in the art will readily appreciate from thedisclosure of the present invention, processes, machines, manufacture,compositions of matter, means, methods, or steps, presently existing orlater to be developed that perform substantially the same function orachieve substantially the same result as the corresponding embodimentsdescribed herein may be utilized according to the present invention.Accordingly, the appended claims are intended to include within theirscope such processes, machines, manufacture, compositions of matter,means, methods, or steps. The invention disclosed herein may suitably bepracticed in the absence of any element that is not specificallydisclosed herein.

1. A V-belt having a number of upper cogs and upper roots with upperpitch and upper curvilinear profile, a number of lower cogs and lowerroots with lower pitch and lower curvilinear profile, and a reinforcingtensile layer substantially midway between the upper roots and the lowerroots; with the upper profile symmetric and comprising lines (“L”) andarcs (“A”) connected according to the sequence L1-A1-L2-A2-L3 from thecenter of any of said upper roots to the center of an adjacent cog ofsaid upper cogs; with the lower profile symmetric and comprising linesand arcs connected according to the sequence A3-L5-A4-L6 from the centerof any of said lower roots to the center of an adjacent cog of saidlower cogs; and with the sum of the length of L1 plus the radius of A1equal to or within 20% of the radius of A3; and with at least one ofsaid upper roots being substantially aligned with at least one of saidlower roots; and with both side surfaces of the V-belt including bothupper and lower cogs cut at an angle α/2 with respect to the verticalaxis of the belt, and with a in the range of approximately 15° to 50° .2. The V-belt of claim 1 wherein said lines L1 and L2 connecttangentially with arc A1, and said line L5 connects tangentially withsaid arc A3.
 3. The V-belt of claim 1 wherein the sum of the length ofL1 plus the radius of A1 is equal to or within 20% greater than theradius of A3.
 4. The V-belt of claim 1 wherein the included angle of theopposing flanks defined by L5 of a lower cog is in the range of 10 to 30degrees, and the included angle of the opposing flanks defined by L2 ofan upper cog is in the range of 10 to 30 degrees.
 5. The V-belt of claim1 wherein the number of upper cogs and lower cogs are equal, and theupper and lower profiles are substantially aligned root-to-root.
 6. TheV-belt of claim 5 wherein the sum of the length of L1 plus the radius ofA1 is equal to or within 20% greater than the radius of A3.
 7. TheV-belt of claim 6 wherein said lines L1 and L2 connect tangentially witharc A1, and said line L5 connects tangentially with arc A3.
 8. TheV-belt of claim 7 wherein the included angle of the opposing flanksdefined by L5 of a lower cog is in the range of 10 to 30 degrees, andthe included angle of the opposing flanks defined by L2 of an upper cogis in the range of 10 to 30 degrees.
 9. The V-belt of claim 8 whereineach adjacent arc and line of both the upper and the lower profile areconnected tangentially.
 10. The V-belt of claim 5 wherein the belt has atop width that is about twice the overall thickness.
 11. The V-belt ofclaim 5 wherein each adjacent arc and line of both the upper and thelower profile connect tangentially.
 12. The V-belt of claim 1 whereinthe number of upper cogs is greater than the number of lower cogs. 13.The V-belt of claim 12 wherein the number of upper cogs is about 1.1 to1.3times the number of lower cogs.
 14. The V-belt of claim 12 whereinsaid lines L1 and L2 connect tangentially with arc A1, and said line L5connects tangentially with arc A3.
 15. The V-belt of claim 12 whereinthe included angle of the opposing flanks defined by L5 of a lower cogis in the range of 10 to 30 degrees, and the included angle of theopposing flanks defined by L2 of an upper cog is in the range of 10 to30 degrees.
 16. The V-belt of claim 12 wherein the belt has a top widththat is about twice the overall thickness.
 17. The V-belt of claim 12wherein each adjacent arc and line of both the upper and the lowerprofile connect tangentially.
 18. The V-belt of claim 1 furthercomprising opposing side surfaces having a relief angle disposed near alower cog tip.
 19. The V-belt of claim 1 wherein the belt has a topwidth that is about twice the overall thickness.
 20. The V-belt of claim1 wherein each adjacent arc and line of both the upper and the lowerprofile connect tangentially.
 21. The V-belt of claim 1 wherein at leastone of said arcs A1, A2, A3, and A4 has an arc radius of at least 1 mm.22. The V-belt of claim 21 wherein each of said arcs A1, A2, A3, and A4has an arc radius of at least 1 mm.
 23. The V-belt of claim 1 whereinsaid upper cogs have an upper cog height H2, and said lower cogs have alower cog height Hl, such that H2 is less than Hl.
 24. The V-belt ofclaim 1 wherein the radius of said arc A1 is greater than the radius ofsaid arc A2, and the radius of said arc A4 is greater than the radius ofsaid arc A3.
 25. The V-belt of claim 24 wherein each of said arcs A1,A2, A3, and A4 has an arc radius of at least 1 mm; and wherein saidupper cogs have an upper cog height H2, and said lower cogs have a lowercog height H1, such that H2 is less than Hl.
 26. A V-belt having anumber of upper cogs and upper roots with upper pitch and uppercurvilinear profile, a number of lower cogs and lower roots with lowerpitch and lower curvilinear profile, and a reinforcing tensile layersubstantially midway between the upper roots and the lower roots; withthe upper profile symmetric and comprising lines (“L”) and arcs (“A”)connected according to the sequence L1-A1-A2-L3 from the center of anyof said upper roots to the center of an adjacent cog of said upper cogs;with the lower profile symmetric and comprising lines and arcs connectedaccording to the sequence L4-A3-L5-A4-L6 from the center of any of saidlower roots to the center of an adjacent cog of said lower cogs; andwith the sum of the length of L1 plus the radius of A1 equal to orwithin 20% of the radius of A3; and with at least one of said upperroots being substantially aligned with at least one of said lower roots.